Question

if two complementary angles have the ratio of 2 to 6, find the value of each angle. 71.5° 26.5° 21° 67.5° 22.5° 66°

Explanation:

Step1: Set up the equation

Let the angles be \(2x\) and \(6x\). Since they are complementary, \(2x + 6x=90^{\circ}\).

Step2: Solve for \(x\)

Combine like terms: \(8x = 90^{\circ}\). Then \(x=\frac{90^{\circ}}{8}=11.25^{\circ}\).

Step3: Find the angles

First angle: \(2x=2\times11.25^{\circ}=22.5^{\circ}\). Second angle: \(6x = 6\times11.25^{\circ}=67.5^{\circ}\).

Answer:

\(22.5^{\circ}\), \(67.5^{\circ}\)